There are three possible ways to become a captain.
- Having Bankai and show it openly. This has to be displayed in front of the Captain-Commander (Yama-jii), and two other captains.
- Get the approval of 6 captains and the affirmation of three captains, including the Captain-Commander...
- Defeating the current captain with 200 witnesses of that specific division.
While most captains have bankai, this is not a prerequisite if you use methods 2 or 3. It is clearly stated that one of the captains, Zaraki Kenpachi, does not have bankai so he used method 3. It is very unlikely that someone could become a captain without bankai, but there is clear precendent. On the other hand, right now there are so many captain openings that they might let weaklings without bankai, like Kira, become a captain through method 2.